Let’s say you and I are both trying to see the same top-rated surgeon, and because I’m willing to pay extra, it takes me 24 hours to get an appointment that you need to wait six months for. Would that be upsetting?

Now let’s say that even though you have the best insurance available, if you can’t pay the entire cost up front then that same surgeon won’t see you at all, no matter how long you wait. What about now?

While health wonks have been focused on the effects of Obamacare, another change has been happening, intertwined with the new law but worth thinking about separately: How is growing income inequality affecting the delivery of health care? And is that change for the better?

A few weeks ago, I got an e-mail from Mark Hadfield, founder and chief executive officer of HelloMD, a company that connects patients with the best doctors in San Francisco, Los Angeles and Las Vegas, as determined through a selection process. HelloMD offers faster appointments than regular patients can get, for a price: Its customers pay the doctors higher rates than insurance plans offer. And they pay those rates in cash.

Better access for well-heeled patients isn’t new, of course. Concierge medicine, in which people pay an annual fee for focused care from primary care doctors, has existed for years. What makes HelloMD different, according to Hadfield, is its focus on specialty care. Rather than assembling a small group of doctors under one roof, HelloMD is a portal to the top specialists in every field, letting you buy your way to the front of the line.

Hadfield said his service is as attractive for doctors as it is for patients, and it’s not hard to see why. Under HelloMD’s model, doctors are not only released from the hassle of seeking reimbursement from health plans (the “insurance-doctor dystopia,” as Hadfield put it) but also free to set their own rates.

How high are those rates? Hadfield said he expects it to vary widely, and suggested that the premiums over insurer-negotiated rates might average 30 percent. That may be low. Nicholas Colyvas, an orthopedic specialist in San Francisco who takes patients through HelloMD, told me he expects a difference of closer to 50 percent, and even 100 percent in some cases.

The difference from what a patient with insurance would actually pay out of pocket is much greater than that. Colyvas said he sets his cash prices for a consultation at $300 to $350. A typical copayment to see a specialist could be as low as $40. (Patients with insurance can try to get their health plan to reimburse part of what they’ve paid, but good luck getting a significant part of that cost covered.) Sure enough, when I asked Colyvas what distinguishes his cash-only patients, he said they shared just one important characteristic: They’re all wealthy.

It’s hard to object to people paying more to see doctors quickly; the practice may seem unfair, but no more so than for any other type of service. Colyvas emphasized that he wouldn’t make somebody wait longer for emergency care just because they can’t pay in cash. So long as others aren’t deprived of the care they need because a cash patient jumped the queue, the worst you can say is that it’s obnoxious.

Things get trickier if the best specialists become altogether unavailable to patients who can’t afford to pay in cash. Hadfield said that while many of the specialists continue to see patients with traditional insurance, more would like to switch entirely to cash only. Cash patients make up about 10 percent of Colyvas’s practice now; he said his ideal mix is 100 percent.

It’s unclear how far the U.S. health-care system will move in that direction. The slice of the population that’s able to pay for specialty care in cash is small; the share of physicians in cash-only practices was just 6 percent last year.

But that’s double the level from 2011. And if the income gap keeps growing, so will the number of doctors who can find enough cash-only patients to stop taking insurance. Another factor is Obamacare: Expanding health coverage to millions of Americans will put pressure on the supply of physicians, at least initially. Some people who don’t want to pay cash today may decide later that the extra cost is worth it for faster appointments.

If the trend accelerates, it may call for new guidelines from the American Medical Association. The AMA now says doctors moving to cash-only practices must “facilitate the transfer of their non-participating patients to other physicians” — for instance, not charging for the transfer of medical records.

If no other physicians are available in the community, the doctor “may be ethically obligated to continue caring for such patients.” The AMA also reminds doctors of their “professional obligation to provide care to those in need.” Those guidelines may start to look too vague if the best specialists drop out of the insurance system altogether.

If HelloMD and similar services gain popularity, they’ll add new emphasis to the endless American debate over access to health care: When is the gap between rich and poor too big?